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NCERT Solutions for Class 11 Maths Chapter 1 Sets are discussd here. In our daily life, we have come across situations like arranging books on a shelf with different categories like novels, short stories, science fiction, etc. The well-defined collection of objects is called a set. In this article, you will get class 11 sets NCERT solutions. This chapter sets class 11 will introduce the concept of sets and different operations on set. Check NCERT solutions that are created by Careers360 Expert team according to latest update on the CBSE syllabus 2023. The knowledge of sets is also required to study geometry, sequences, probability, etc. NCERT solutions for class 11 maths chapter 1 sets will build your basics of data analysis which will be useful in higher education.
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Sets play a crucial role in defining functions and relations, concepts which are introduced in Chapter 1 of the NCERT textbook for Class 11 Maths, as per the CBSE syllabus. This chapter covers fundamental definitions and operations involving sets. Having a sound understanding of sets is imperative for studying sequences, geometry, and probability. Although it is an essential chapter, it is comparatively easier than other chapters in the NCERT Class 11 Maths textbook, making it an opportunity to score maximum marks in the board examination. Here students can find all NCERT solution for Class 11 . The NCERT solutions for class 11 maths chapter 1 set will improve the basics of sets which will be useful in further mathematics courses also.
Also read:
Union of Sets (A∪B): A∪B
Intersection of Sets (A∩B): A∩B
Complement of a Set (A'): A'
De Morgan’s Theorem:
(A∪B)' = A'∩B'
(A∩B)' = A'∪B'
Set Cardinality with Intersection:
n(A∪B) = n(A) + n(B)
n(A∪B) = n(A) + n(B) - n(A∩B)
Other Set Formulas:
A - A = Ø
B - A = B∩A'
B - A = B - (A∩B)
(A - B) = A if A∩B = Ø
(A - B) ∩ C = (A∩ C) - (B∩C)
A ΔB = (A-B) ∪ (B-A)
n(A∪B∪C) = n(A) + n(B) + n(C) - n(B∩C) - n(A∩B) - n(A∩C) + n(A∩B∩C)
n(A - B) = n(A∪B) - n(B)
n(A - B) = n(A) - n(A∩B)
n(A') = n(U) - n(A)
n(U) = n(A) + n(B) - n(A∩B)
n((A∪B)') = n(U) + n(A∩B) - n(A) - n(B)
Free download NCERT Solutions for Class 11 Maths Chapter 1 Sets for CBSE Exam.
NCERT sets class 11 questions and answers - Exercise: 1.1
Question:1(i) Which of the following are sets ? justify your answer
The collection of all the months of a year beginning with the letter J.
Answer:
The months starting with letter J are:
january
june
july
Hence,this is collection of well defined objects so it is a set.
Question:1(ii) Which of the following are sets ? justify your answer
The collection of ten most talented writers of India.
Answer:
Ten most talented writers may be different depending on different criteria of determining talented writers.
Hence, this is not well defined so cannot be a set.
Question:1(iii) Which of the following are sets ? justify your answer
A team of eleven best-cricket batsmen of the world.
Answer:
Eleven most talented cricketers may be different depending on criteria of determining talent of a player.
Hence,this is not well defined so it is not a set.
Question:1(iv) Which of the following are sets ? justify your answer
The collection of all boys in your class.
Answer:
The collection of boys in a class are well defined and known.
Group of well defined objects is a set.
Hence, it is a set.
Question:1(v) Which of the following are sets ? justify your answer
The collection of all natural numbers less than 100.
Answer:
Natural numbers less than 100 has well defined and known collection of numbers.
that is S= {1,2,3............99}
Hence,it is a set.
Question:1(vi) Which of the following are sets? Justify your answer
A collection of novels written by the writer Munshi Prem Chand.
Answer:
The collection of novels written by Munshi Prem Chand is well defined and known .
Hence,it is a set.
Question:1(vii) Which of the following are sets? Justify your answer
The collection of all even integers.
Answer:
The collection of even intergers is well defined because we can get even integers till infinite. that is
Hence,it is a set.
Question:1(viii) Which of the following are sets? Justify your answer
The collection of questions in this Chapter.
Answer:
Collection of questions in a chapter is well defined and known .
Hence ,it is a set.
Question:1(ix) Which of the following are sets? Justify your answer
A collection of most dangerous animals of the world.
Answer:
A Collection of most dangerous animal is not well defined because the criteria of defining dangerousness of any animal can vary .
Hence,it is not a set.
(ii) 8_____A
(iii) 0_____A
(iv) 4_____A
(v) 2_____A
(vi) 10____A
Answer:
A = ,the elements which lie in this set belongs to this set and others do not belong.
(i) 5 A
(ii) 8 A
(iii) 0 A
(iv) 4 A
(v) 2 A
(vi) 10 A
Question:3(i) Write the following sets in roster form
Answer:
Elements of this set are:-3,-2,-1,0,1,2,3,4,5,6.
Hence ,this can be written as:
A =
Question:3(ii) Write the following sets in roster form
Answer:
Natural numbers less than 6 are: 1,2,3,4,5.
This can be written as:
Question:3(iii) Write the following sets in roster form
C = {x : x is a two-digit natural number such that the sum of its digits is 8}
Answer:
The two digit numbers having sum equal to 8 are: 17,26,35,44,53,62,71,80.
This can be written as:
Question:3(iv) Write the following sets in roster form
D = {x : x is a prime number which is divisor of 60}
Answer:
Prime numbers which are divisor of 60 are:2,3,5.
This can be written as:
Question:3(v) Write the following sets in roster form
E = The set of all letters in the word TRIGONOMETRY.
Answer:
Letters of word TRIGONOMETRY are: T, R, I, G, N, O, M, E, Y.
This can be written as :
E = {T,R,I,G,N,O,M,E,Y}
Question:3(vi) Write the following sets in roster form
F = The set of all letters in the word BETTER.
Answer:
The set of letters of word BETTER are: {B,E,T,R}
This can be written as:
F = {B,E,T,R}
Question:4(i) Write the following sets in the set builder form
{3, 6, 9, 12}
Answer:
A = {3,6,9,12}
This can be written as :
Question:4(ii) Write the following sets in the set builder form
{2,4,8,16,32}
Answer:
can be written as
Question:4(iii) Write the following sets in the set builder form:
{5, 25, 125, 625}
Answer:
can be written as
Question:4(iv) Write the following sets in the set builder form:
{2, 4, 6, . . .}
Answer:
This is a set of all even natural numbers.
{2,4,6....} can be written as {x : x is an even natural number}
Question:4(v) Write the following sets in the set builder form :
{1,4,9, . . .,100}
Answer:
.
.
.
.
can be written as
Question:5(i) List all the elements of the following sets:
A = {x : x is an odd natural number}.
Answer:
A = { x : x is an odd natural number } = {1,3,5,7,9,11,13.............}
Question:5(ii) List all the elements of the following sets:
B= { x : x is an integer, }
Answer:
Intergers between are 0,1,2,3,4.
Hence,B = {0,1,2,3,4}
Question:5(iii) List all the elements of the following sets:
C = {x : x is an integer, }
Answer:
Integers whose square is less than or equal to 4 are : -2,-1,0,1,2.
Hence,it can be written as c = {-2,-1,0,1,2}.
Question:5(iv) List all the elements of the following sets:
D = {x : x is a letter in the word “LOYAL”}
Answer:
LOYAL has letters L,O,Y,A.
D = {x : x is a letter in the word “LOYAL”} can be written as {L,O,Y,A}.
Question:5(v) List all the elements of the following sets:
E = {x : x is a month of a year not having 31 days}
Answer:
The months not having 31 days are:
February
April
June
September
November
It can be written as {february,April,June,September,november}
Question:5(vi) List all the elements of the following sets :
F = {x : x is a consonant in the English alphabet which precedes k }.
Answer:
The consonents in english which precedes K are : B,C,D,F,G,H,J
Hence, F = {B,C,D,F,G,H,J}.
(i) {1, 2, 3, 6} (a) {x : x is a prime number and a divisor of 6}
(ii) {2, 3} (b) {x : x is an odd natural number less than 10}
(iii) {M,A,T,H,E,I,C,S} (c) {x : x is natural number and divisor of 6}
(iv) {1, 3, 5, 7, 9} (d) {x : x is a letter of the word MATHEMATICS}.
Answer:
(i) 1,2,3,6 all are natural numbers and also divisors of 6.
Hence,(i) matches with (c)
(ii) 2,3 are prime numbers and are divisors of 6.
Hence,(ii) matches with (a).
(iii) M,A,T,H,E,I,C,S are letters of word "MATHEMATICS".
Hence, (iii) matches with (d).
(iv) 1,3,5,7,9 are odd natural numbers less than 10.
Hence,(iv) matches with (b).
NCERT class 11 maths chapter 1 question answer sets-Exercise: 1.2
Question:1(i) Which of the following are examples of the null set :
Set of odd natural numbers divisible by 2
Answer:
No odd number is divisible by 2.
Hence, this is a null set.
Question:1(ii) Which of the following are examples of the null set :
Set of even prime numbers.
Answer:
Even prime number = 2.
Hence, it is not a null set.
Question:1(iii) Which of the following are examples of the null set:
{ x : x is a natural numbers, and }
Answer:
No number exists which is less than 5 and more than 7.
Hence, this is a null set.
Question:1(iv) Which of the following are examples of the null set :
{ y : y is a point common to any two parallel lines}
Answer:
Parallel lines do not intersect so they do not have any common point.
Hence, it is a null set.
Question:2 Which of the following sets are finite or infinite:
(i) The set of months of a year
(ii) {1, 2, 3, . . .}
(iii) {1, 2, 3, . . .99, 100}
(iv) ) The set of positive integers greater than 100.
(v) The set of prime numbers less than 99
Answer:
(i) Number of months in a year are 12 and finite.
Hence,this set is finite.
(ii) {1,2,3,4.......} and so on ,this does not have any limit.
Hence, this is infinite set.
(iii) {1,2,3,4,5......100} has finite numbers.
Hence ,this is finite set.
(iv) Positive integers greater than 100 has no limit.
Hence,it is infinite set.
(v) Prime numbers less than 99 are finite ,known numbers.
Hence,it is finite set.
Question:3 State whether each of the following set is finite or infinite:
(i) The set of lines which are parallel to the x-axis
(ii) The set of letters in the English alphabet
(iii) The set of numbers which are multiple of 5
(iv) The set of animals living on the earth
(v) The set of circles passing through the origin (0,0)
Answer:
(i) Lines parallel to the x-axis are infinite.
Hence, it is an infinite set.
(ii) Letters in English alphabets are 26 letters which are finite.
Hence, it is a finite set.
(iii) Numbers which are multiple of 5 has no limit, they are infinite.
Hence, it is an infinite set.
(iv) Animals living on earth are finite though the number is very high.
Hence, it is a finite set.
(v) There is an infinite number of circles which pass through the origin.
Hence, it is an infinite set.
Question:4(i) In the following, state whether A = B or not:
A = { a, b, c, d } B = { d, c, b, a }
Answer:
Given
A = {a,b,c,d}
B = {d,c,b,a}
Comparing the elements of set A and set B, we conclude that all the elements of A and all the elements of B are equal.
Hence, A = B.
Question:4(ii) In the following, state whether A = B or not:
A = { 4, 8, 12, 16 } B = { 8, 4, 16, 18}
Answer:
12 belongs A but 12 does not belong to B
12 A but 12 B.
Hence, A B.
Question:4(iii) In the following, state whether A = B or not:
A = {2, 4, 6, 8, 10} B = { x : x is positive even integer and }
Answer:
Positive even integers less than or equal to 10 are : 2,4,6,8,10.
So, B = { 2,4,6,8,10 } which is equal to A = {2,4,6,8,10}
Hence, A = B.
Question:4(iv) In the following, state whether A = B or not:
A = { x : x is a multiple of 10}, B = { 10, 15, 20, 25, 30, . . . }
Answer:
Multiples of 10 are : 10,20,30,40,........ till infinite.
SO, A = {10,20,30,40,.........}
B = {10,15,20,25,30........}
Comparing elements of A and B,we conclude that elements of A and B are not equal.
Hence, A B.
Question:5(i) Are the following pair of sets equal ? Give reasons.
A = {2, 3}, B = {x : x is solution of + 5x + 6 = 0}
Answer:
As given,
A = {2,3}
And,
x = -2 and -3
B = {-2,-3}
Comparing elements of A and B,we conclude elements of A and B are not equal.
Hence,A B.
Question:5(ii) Are the following pair of sets equal ? Give reasons.
A = { x : x is a letter in the word FOLLOW}
B = { y : y is a letter in the word WOLF}
Answer:
Letters of word FOLLOW are F,OL,W.
SO, A = {F,O,L,W}
Letters of word WOLF are W,O,L,F.
So, B = {W,O,L,F}
Comparing A and B ,we conclude that elements of A are equal to elements of B.
Hence, A=B.
Question:6 From the sets given below, select equal sets :
A = { 2, 4, 8, 12}, B = { 1, 2, 3, 4}, C = { 4, 8, 12, 14}, D = { 3, 1, 4, 2}
E = {–1, 1}, F = { 0, a}, G = {1, –1}, H = { 0, 1}
Answer:
Compare the elements of A,B,C,D,E,F,G,H.
8 A but
Now, 2 A but 2 C.
Hence, A B,A C,A D,A E,A F,A G,A H.
3 B,3 D but 3 C,3 E,3 F,3 G,3 H.
Hence,B C,B E,B F,B G,B H.
Similarly, comparing other elements of all sets, we conclude that elements of B and elements of D are equal also elements of E and G are equal.
Hence, B=D and E = G.
NCERT class 11 maths chapter 1 question answer sets - Exercise: 1.3
Question:1 Make correct statements by filling in the symbols or in the blank spaces :
(i) { 2, 3, 4 } _____ { 1, 2, 3, 4,5 }
(ii) { a, b, c }______ { b, c, d }
(iii) {x : x is a student of Class XI of your school}______{x : x student of your school}
(iv) {x : x is a circle in the plane} ______{x : x is a circle in the same plane with radius 1 unit}
(v) {x : x is a triangle in a plane} ______ {x : x is a rectangle in the plane}
(vi) {x : x is an equilateral triangle in a plane} ______{x : x is a triangle in the same plane}
(vii) {x : x is an even natural number} _____ {x : x is an integer}
Answer:
A set A is said to be a subset of a set B if every element of A is also an element of B.
(i). All elements {2,3,4} are also elements of {1,2,3,4,5} .
So, {2,3,4} {1,2,3,4,5}.
(ii).All elements { a, b, c } are not elements of{ b, c, d }.
Hence,{ a, b, c } { b, c, d }.
(iii) Students of class XI are also students of your school.
Hence,{x : x is a student of Class XI of your school} {x : x student of your school}
(iv). Here, {x : x is a circle in the plane} {x : x is a circle in the same plane with radius 1 unit} : since a circle in the plane can have any radius
(v). Triangles and rectangles are two different shapes.
Hence,{x : x is a triangle in a plane} {x : x is a rectangle in the plane}
(vi). Equilateral triangles are part of all types of triangles.
So,{x : x is an equilateral triangle in a plane} {x : x is a triangle in the same plane}
(vii).Even natural numbers are part of all integers.
Hence, {x : x is an even natural number} {x : x is an integer}
Question:2 Examine whether the following statements are true or false:
(i) { a, b } { b, c, a }
(ii) { a, e } { x : x is a vowel in the English alphabet}
(iii) { 1, 2, 3 } { 1, 3, 5 }
(iv) { a } { a, b, c }
(v) { a } { a, b, c }
(vi) { x : x is an even natural number less than 6} { x : x is a natural number which divides 36}
Answer:
(i) All elements of { a, b } lie in { b, c, a }.So,{ a, b } { b, c, a }.
Hence,it is false.
(ii) All elements of { a, e } lie in {a,e,i,o,u}.
Hence,the statements given is true.
(iii) All elements of { 1, 2, 3 } are not present in { 1, 3, 5 }.
Hence,statement given is false.
(iv) Element of { a } lie in { a, b, c }.
Hence,the statement is true.
(v). { a } { a, b, c }
So,the statement is false.
(vi) All elements {2,4,} lies in {1,2,3,4,6,9,12,18,36}.
Hence,the statement is true.
Question:3(i) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?
{3, 4} A
Answer:
3 {3,4} but 3 {1,2,{3,4},5}.
SO, {3, 4} A
Hence,the statement is incorrect.
Question:3(ii) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?
{3, 4} A
Answer:
{3, 4} is element of A.
So, {3, 4} A.
Hence,the statement is correct.
Question:3(iii) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?
{{3, 4}} A
Answer:
Here,
{ 3, 4 } { 1, 2, { 3, 4 }, 5 }
and { 3, 4 } {{3, 4}}
So, {{3, 4}} A.
Hence,the statement is correct.
Question:3(iv) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?
1 A
Answer:
Given, 1 is element of { 1, 2, { 3, 4 }, 5 }.
So,1 A.
Hence,statement is correct.
Question:3(v) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?
1 A
Answer:
Here, 1 is element of set A = { 1, 2, { 3, 4 }, 5 }.So,elements of set A cannot be subset of set A.
1 { 1, 2, { 3, 4 }, 5 }.
Hence,the statement given is incorrect.
Question:3(vi) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?
{1,2,5} A
Answer:
All elements of {1,2,5} are present in { 1, 2, { 3, 4 }, 5 }.
So, {1,2,5} { 1, 2, { 3, 4 }, 5 }.
Hence,the statement given is correct.
Question:3(vii) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?
{1,2,5} A
Answer:
Here,{1,2,5} is not an element of { 1, 2, { 3, 4 }, 5 }.
So,{1,2,5} A .
Hence, statement is incorrect.
Question:3(viii) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?
{1,2,3} A
Answer:
Here, 3 {1,2,3}
but 3 { 1, 2, { 3, 4 }, 5 }.
So, {1,2,3} A
Hence,the given statement is incorrect.
Question:3(ix) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?
Answer:
is not an element of { 1, 2, { 3, 4 }, 5 }.
So, .
Hence,the above statement is incorrect.
Question:3(x) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?
Answer:
is subset of all sets.
Hence,the above statement is correct.
Question:3(xi) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?
Answer:
{ 1, 2, { 3, 4 }, 5 }. but is not an element of { 1, 2, { 3, 4 }, 5 }.
Hence, the above statement is incorrect.
Question:4(ii) Write down all the subsets of the following sets:
{a, b}
Answer:
Subsets of . Thus the given set has 4 subsets
Question:4(iv) Write down all the subsets of the following sets:
Answer:
Subset of is only.
The subset of a null set is null set itself
Question:5 How many elements has P(A), if A = ?
Answer:
Let the elements in set A be m, then n m
then, the number of elements in power set of A n
Here, A = so n 0
n 1
Hence,we conclude P(A) has 1 element.
Question:6 Write the following as intervals :
(i) {x : x R, – 4 x 6}
(ii) {x : x R, – 12 x –10}
(iii) {x : x R, 0 x 7}
(iv) {x : x R, 3 x 4}
Answer:
The following can be written in interval as :
(i) {x : x R, – 4 x 6}
(ii) {x : x R, – 12 x –10}
(iii) {x : x R, 0 x 7}
(iv) (iv) {x : x R, 3 x 4}
Question:7 Write the following intervals in set-builder form :
(i) (– 3, 0)
(ii) [6 , 12]
(iii) (6, 12]
(iv) [–23, 5)
Answer:
The given intervals can be written in set builder form as :
(i) (– 3, 0)
(ii) [6 , 12]
(iii) (6, 12]
(iv) [–23, 5)
Question:8 What universal set(s) would you propose for each of the following :
(i) The set of right triangles.
(ii) The set of isosceles triangles.
Answer:
(i) Universal set for a set of right angle triangles can be set of polygons or set of all triangles.
(ii) Universal set for a set of isosceles angle triangles can be set of polygons.
NCERT class 11 maths chapter 1 question answer sets - Exercise: 1.4
Question:1(i) Find the union of each of the following pairs of sets :
X = {1, 3, 5} Y = {1, 2, 3}
Answer:
Union of X and Y is X Y = {1,2,3,5}
Question:1(ii) Find the union of each of the following pairs of sets :
A = [ a, e, i, o, u} B = {a, b, c}
Answer:
Union of A and B is A B = {a,b,c,e,i,o,u}.
Question:1(iii) Find the union of each of the following pairs of sets :
A = {x : x is a natural number and multiple of 3} B = {x : x is a natural number less than 6}
Answer:
Here ,
A = {3,6,9,12,15,18,............}
B = {1,2,3,4,5,6}
Union of A and B is A B.
A B = {1,2,3,4,5,6,9,12,15........}
Question:1(iv) Find the union of each of the following pairs of sets :
A = {x : x is a natural number and 1 x 6 }
B = {x : x is a natural number and 6 x 10 }
Answer:
Here,
A = {2,3,4,5,6}
B = {7,8,9}
A B = {2,3,4,5,6,7,8,9}
or it can be written as A B = {x : x is a natural number and 1 x 10 }
Question:1(v) Find the union of each of the following pairs of sets :
A = {1, 2, 3} B =
Answer:
Here,
A union B is A B.
A B = {1,2,3}
Question:2 Let A = { a, b }, B = {a, b, c}. Is A B ? What is A B ?
Answer:
Here,
We can see elements of A lie in set B.
Hence, A B.
And, A B = {a,b,c} = B
Question:3 If A and B are two sets such that A B, then what is A B ?
Answer:
If A is subset of B then A B will be set B.
Question:4(i) If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = { 7, 8, 9, 10 }; find
A B
Answer:
Here,
A = {1, 2, 3, 4}
B = {3, 4, 5, 6}
The union of the set can be written as follows
A B = {1,2,3,4,5,6}
Question:4(ii) If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = { 7, 8, 9, 10 }; find
A C
Answer:
Here,
A = {1, 2, 3, 4}
C = {5, 6, 7, 8 }
The union can be written as follows
A C = {1,2,3,4,5,6,7,8}
Question:4(iii) If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = { 7, 8, 9, 10 }; find
B C
Answer:
Here,
B = {3, 4, 5, 6},
C = {5, 6, 7, 8 }
The union of the given sets are
B C = { 3,4,5,6,7,8}
Question:4(iv) If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = { 7, 8, 9, 10 }; find
B D
Answer:
Here,
B = {3, 4, 5, 6}
D = { 7, 8, 9, 10 }
B D = {3,4,5,6,7,8,9,10}
Question: 4(v) If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = { 7, 8, 9, 10 }; find
A B C
Answer:
Here,
A = {1, 2, 3, 4},
B = {3, 4, 5, 6},
C = {5, 6, 7, 8 }
The union can be written as
A B C = {1,2,3,4,5,6,7,8}
Question:4(vi) If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = { 7, 8, 9, 10 }; find
A B D
Answer:
Here,
A = {1, 2, 3, 4},
B = {3, 4, 5, 6}
D = { 7, 8, 9, 10 }
The union can be written as
A B D = {1,2,3,4,5,6,7,8,9,10}
Question:4(vii) If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = { 7, 8, 9, 10 }; find
B C D
Answer:
Here,B = {3, 4, 5, 6},
C = {5, 6, 7, 8 } and
D = { 7, 8, 9, 10 }
The union can be written as
B C D = {3,4,5,6,7,8,9,10}
Question:5 Find the intersection of each pair of sets of question 1 above
(i) X = {1, 3, 5} Y = {1, 2, 3}
(ii) A = [ a, e, i, o, u} B = {a, b, c}
(iii) A = {x : x is a natural number and multiple of 3} B = {x : x is a natural number less than 6}
(iv) A = {x : x is a natural number and 1 x 6 } B = {x : x is a natural number and 6 x 10 }
Answer:
(i) X = {1, 3, 5} Y = {1, 2, 3}
X Y = {1,3}
(ii) A = [ a, e, i, o, u} B = {a, b, c}
A B = {a}
(iii) A = {x : x is a natural number and multiple of 3} B = {x : x is a natural number less than 6}
A = {3,6,9,12,15.......} B = {1,2,3,4,5}
A B = {3}
(iv)A = {x : x is a natural number and 1 x 6 } B = {x : x is a natural number and 6 x 10 }
A = {2,3,4,5,6} B = {7,8,9}
A B =
(v) A = {1, 2, 3}, B =
A B =
Question:6 If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15}and D = {15, 17}; find
(i) A B (ii) B C
(iii) A C D (iv) A C
(v) B D (vi) A (B C)
(vii) A D (viii) A (B D)
(ix) ( A B ) ( B C ) (x) ( A D) ( B C)
Answer:
Here, A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}
(i) A B = {7,9,11} (vi) A (B C) = {7,9,11}
(ii) B C = { 11,13} (vii) A D =
(iii) A C D = (viii) A (B D) = {7,9,11}
(iv) A C = { 11 } (ix) ( A B ) ( B C ) = {7,9,11}
(v) B D = (x) ( A D) ( B C) = {7,9,11,15}
(i) A B
(ii) A C
(iii) A D
(iv) B C
(v) B D
(vi) C D
Answer:
Here, A = {1,2,3,4,5,6...........}
B = {2,4,6,8,10...........}
C = {1,3,5,7,9,11,...........}
D = {2,3,5,7,11,13,17,......}
(i) A B = {2,4,6,8,10........} = B
(ii) A C = {1,3,5,7,9.........} = C
(iii) A D = {2,3,5,7,11,13.............} = D
(iv) B C =
(v) B D = {2}
(vi) C D = {3,5,7,11,13,..........} =
Question:8(i) Which of the following pairs of sets are disjoint
{1, 2, 3, 4} and {x : x is a natural number and 4 x 6 }
Answer:
Here, {1, 2, 3, 4} and {4,5,6}
{1, 2, 3, 4} {4,5,6} = {4}
Hence,it is not a disjoint set.
Question:8(ii) Which of the following pairs of sets are disjoint
{ a, e, i, o, u } and { c, d, e, f }
Answer:
Here, { a, e, i, o, u } and { c, d, e, f }
{ a, e, i, o, u } { c, d, e, f } = {e}
Hence,it is not disjoint set.
Question:8(iii) Which of the following pairs of sets are disjoint
{x : x is an even integer } and {x : x is an odd integer}
Answer:
Here, {x : x is an even integer } and {x : x is an odd integer}
{2,4,6,8,10,..........} and {1,3,5,7,9,11,.....}
{2,4,6,8,10,..........} {1,3,5,7,9,11,.....} =
Hence,it is disjoint set.
(i) A – B (ii) A – C (iii) A – D (iv) B – A (v) C – A (vi) D – A
(vii) B – C (viii) B – D (ix) C – B (x) D – B (xi) C – D (xii) D – C
Answer:
A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }
The given operations are done as follows
(i) A – B = {3,6,9,15,18,21} (vii) B – C = {20}
(ii) A – C = {3,9,15,18,21} (viii) B – D = {4,8,12,16}
(iii) A – D = {3,6,9,12,18,21} (ix) C – B = {2,6,10,14}
(iv) B – A = {4,8,16,20} (x) D – B = {5,10,15}
(v) C – A = {2,4,8,10,14,16} (xi) C – D = {2,4,6,8,12,14,16}
(vi) D – A = {5,10,20} (xii) D – C = {5,15,20}
Question:10 If X= { a, b, c, d } and Y = { f, b, d, g}, find
(i) X – Y
(ii) Y – X
(iii) X Y
Answer:
X= { a, b, c, d } and Y = { f, b, d, g}
(i) X – Y = {a,c}
(ii) Y – X = {f,g}
(iii) X Y = {b,d}
Question:11 If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q ?
Answer:
R = set of real numbers.
Q = set of rational numbers.
R - Q = set of irrational numbers.
Question:12(i) State whether each of the following statement is true or false. Justify your answer.
{ 2, 3, 4, 5 } and { 3, 6} are disjoint sets.
Answer:
Here,
{ 2, 3, 4, 5 } and { 3, 6}
{ 2, 3, 4, 5 } { 3, 6} = {3}
Hence,these are not disjoint sets.
So,false.
Question:12(ii) State whether each of the following statement is true or false. Justify your answer.
{ a, e, i, o, u } and { a, b, c, d }are disjoint sets
Answer:
Here, { a, e, i, o, u } and { a, b, c, d }
{ a, e, i, o, u } { a, b, c, d } = {a}
Hence,these are not disjoint sets.
So, statement is false.
Question:12(iii) State whether each of the following statement is true or false. Justify your answer.
{ 2, 6, 10, 14 } and { 3, 7, 11, 15} are disjoint sets.
Answer:
Here,
{ 2, 6, 10, 14 } and { 3, 7, 11, 15}
{ 2, 6, 10, 14 } { 3, 7, 11, 15} =
Hence, these are disjoint sets.
So,given statement is true.
Question:12(iv) State whether each of the following statement is true or false. Justify your answer.
{ 2, 6, 10 } and { 3, 7, 11} are disjoint sets.
Answer:
Here,
{ 2, 6, 10 } and { 3, 7, 11}
{ 2, 6, 10 } { 3, 7, 11} =
Hence,these are disjoint sets.
So,statement is true.
Class 11 maths chapter 1 NCERT solutions sets-Exercise: 1.5
(i) A′
(ii) B′
(iii) (A C)′
(iv) (A B)′
(v) (A')'
(vi) (B – C)'
Answer:
U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = { 1, 2, 3, 4}, B = { 2, 4, 6, 8 } and C = { 3, 4, 5, 6 }
(i) A′ = U - A = {5,6,7,8,9}
(ii) B′ = U - B = {1,3,5,7,9}
(iii) A C = {1,2,3,4,5,6}
(A C)′ = U - (A C) = {7,8,9}
(iv) (A B) = {1,2,3,4,6,8}
(A B)′ = U - (A B) = {5,7,9}
(v) (A')' = A = { 1, 2, 3, 4}
(vi) (B – C) = {2,8}
(B – C)' = U - (B – C) = {1,3,4,5,6,7,9}
Question:2 If U = { a, b, c, d, e, f, g, h}, find the complements of the following sets :
(i) A = {a, b, c}
(ii) B = {d, e, f, g}
(iii) C = {a, c, e, g}
(iv) D = { f, g, h, a}
Answer:
U = { a, b, c, d, e, f, g, h}
(i) A = {a, b, c}
A' = U - A = {d,e,f,g,h}
(ii) B = {d, e, f, g}
B' = U - B = {a,b,c,h}
(iii) C = {a, c, e, g}
C' = U - C = {b,d,f,h}
(iv) D = { f, g, h, a}
D' = U - D = {b,c,d,e}
(i) {x : x is an even natural number}
(ii) { x : x is an odd natural number }
(iii) {x : x is a positive multiple of 3}
(iv) { x : x is a prime number }
(v) {x : x is a natural number divisible by 3 and 5}
Answer:
Universal set = U = {1,2,3,4,5,6,7....................}
(i) {x : x is an even natural number} = {2,4,6,8,..........}
{x : x is an even natural number}'= U - {x : x is an even natural number} = {1,3,5,7,9,..........} = {x : x is an odd natural number}
(ii) { x : x is an odd natural number }' = U - { x : x is an odd natural number } = {x : x is an even natural number}
(iii) {x : x is a positive multiple of 3}' = U - {x : x is a positive multiple of 3} = {x : x , x N and is not a positive multiple of 3}
(iv) { x : x is a prime number }' = U - { x : x is a prime number } = { x : x is a positive composite number and 1 }
(v) {x : x is a natural number divisible by 3 and 5}' = U - {x : x is a natural number divisible by 3 and 5} = {x : x is a natural number not divisible by 3 or 5}
(vi) { x : x is a perfect square }
(vii) { x : x is a perfect cube}
(viii) { x : x + 5 8 }
(ix) { x : 2x + 5 9}
(x) { x : x 7 }
(xi) { x : x N and 2x + 1 10 }
Answer:
Universal set = U = {1,2,3,4,5,6,7,8.............}
(vi) { x : x is a perfect square }' = U - { x : x is a perfect square } = { x : x N and x is not a perfect square }
(vii) { x : x is a perfect cube}' = U - { x : x is a perfect cube} = { x : x N and x is not a perfect cube}
(viii) { x : x + 5 8 }' = U - { x : x + 5 8 } = U - {3} = { x : x N and x 3 }
(ix) { x : 2x + 5 9}' = U - { x : 2x + 5 9} = U -{2} = { x : x N and x 2}
(x) { x : x 7 }' = U - { x : x 7 } = { x : x N and x 7 }
(xi) { x : x N and 2x + 1 10 }' = U - { x : x N and x 9/2 } = { x : x N and x 9/2 }
Question:4 If U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8} and B = { 2, 3, 5, 7}. Verify that
(i) (A B)′ = A′ B′
(ii) (A B)′ = A′ B′
Answer:
U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8} and B = { 2, 3, 5, 7}
(i) (A B)′ = A′ B′
L.H.S = (A B)′ = U - (A B) = {1,9}
R.H.S = A′ B′ = {1,3,5,7,9} {1,4,6,8,9} = {1,9}
L.H.S = R.H.S
Hence,the statement is true.
(ii) (A B)′ = A′ B′
L.H.S = U - (A B) ={1,3,4,5,6,7,8,9}
R.H.S = A′ B′ = {1,3,5,7,9} {1,4,6,8,9} = {1,3,4,5,6,7,8,9}
L.H.S = R.H.S
Hence,the statement is true.
Question:5 Draw appropriate Venn diagram for each of the following :
(i) (A ∪ B)′
(ii) A′ ∩ B′
(iii) (A ∩ B)′
(iv) A′ ∪ B′
Answer:
(i) (A ∪ B)′
(A ∪ B) is in yellow colour
(A ∪ B)′ is in green colour
ii) A′ ∩ B′ is represented by the green colour in the below figure
iii) (A ∩ B)′ is represented by green colour in the below diagram and white colour represents (A ∩ B)
iv) A′ ∪ B′
The green colour represents A′ ∪ B′
Answer:
A' is the set of all triangles whose angle is in other words A' is set of all equilateral triangles.
Question:7 Fill in the blanks to make each of the following a true statement :
(i) A A′
(ii) A
(iii) A A′
(iv) U′ A
Answer:
The following are the answers for the questions
(i) A A′ U
(ii) ′ A A
(iii) A A′
(iv) U′ A
Class 11 maths chapter 1 NCERT solutions sets-Exercise: 1.6
Question:1 If X and Y are two sets such that n ( X ) = 17, n ( Y ) = 23 and n ( X Y ) = 38, find n ( X Y ).
Answer:
n( X ) = 17, n( Y ) = 23 and n( X Y ) = 38
n( X Y ) = n( X ) + n( Y ) - n ( X Y )
38 = 17 + 23 - n ( X Y )
n ( X Y ) = 40 - 38
n ( X Y ) = 2.
Answer:
n( X Y ) = 18
n(X) = 8
n(Y) = 15
n( X Y ) = n(X) + n(Y) - n(X Y)
n(X Y) = 8 + 15 - 18
n(X Y) = 5
Answer:
Hindi speaking = 250 = n(A)
English speakind = 200 = n(B)
Group of people = 400 = n(A B)
People speaking both Hindi and English = n(A B)
n(A B) = n(A) + n(B) - n(A B)
n(A B) = 250 + 200 - 400
n(A B) = 450 - 400
n(A B) = 50
Thus,50 people speak hindi and english both.
Answer:
n(S) = 21
n(T) = 32
n(S T) = 11
n(S T) = n(S) + n(T) - n(S T)
n(S T) = 21 + 32 - 11
n(S T) = 53 - 11
n(S T) = 42
Hence, the set (S T) has 42 elements.
Answer:
n( X Y) = 60
n( X ∩ Y) = 10
n(X) = 40
n( X Y) = n(X) + n(Y) - n( X ∩ Y)
n(Y) = 60 - 40 + 10
n(Y) = 30
Hence,set Y has 30 elements.
Answer:
n(people like coffee) = 37
n(people like tea ) = 52
Total number of people = 70
Total number of people = n(people like coffee) + n(people like tea ) - n(people like both tea and coffee)
70 = 37 + 52 - n(people like both tea and coffee)
n(people like both tea and coffee) = 89 - 70
n(people like both tea and coffee) = 19
Hence,19 people like both coffee and tea.
Answer:
Total people = 65
n(like cricket) = 40
n(like both cricket and tennis) = 10
n(like tennis) = ?
Total people = n(like cricket) + n(like tennis) - n(like both cricket and tennis)
n(like tennis) = 65 - 40 + 10
n(like tennis) = 35
Hence,35 people like tennis.
n (people like only tennis) = n(like tennis) - n(like both cricket and tennis)
n (people like only tennis) = 35 - 10
n (people like only tennis) = 25
Hence,25 people like only tennis.
Answer:
n(french) = 50
n(spanish) = 20
n(speak both french and spanish) = 10
n(speak at least one of these two languages) = n(french) + n(spanish) - n(speak both french and spanish)
n(speak at least one of these two languages) = 50 + 20 - 10
n(speak at least one of these two languages) = 70 -10
n(speak at least one of these two languages) = 60
Hence,60 people speak at least one of these two languages.
NCERT class 11 maths ch 1 question answer sets - Miscellaneous Exercise
Question:1 Decide, among the following sets, which sets are subsets of one and another:
A = { x : x R and x satisfy – 8x + 12 = 0 }, B = { 2, 4, 6 },
C = { 2, 4, 6, 8, . . . }, D = { 6 }.
Answer:
Solution of this equation are – 8x + 12 = 0
( x - 2 ) ( x - 6 ) = 0
X = 2,6
A = { 2,6 }
B = { 2, 4, 6 }
C = { 2, 4, 6, 8, . . . }
D = { 6 }
From the sets given above, we can conclude that A B, A C, D A, D B, D C, B C
Hence, we can say that D A B C
If x A and A B , then x B
Answer:
The given statment is false,
example: Let A = { 2,4 }
B = { 1,{2,4},5}
x be 2.
then, 2 { 2,4 } = x A and { 2,4 } { 1,{2,4},5} = A B
But 2 { 1,{2,4},5} i.e. x B
Question:2(ii) In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If A B and B C , then A C
Answer:
The given statement is false,
Let , A = {1}
B = { 1,2,3}
C = {0,{1,2,3},4}
Here, {1} { 1,2,3} = A B and { 1,2,3} {0,{1,2,3},4} = B C
But, {1} {0,{1,2,3},4} = A C
Question:2(iii) In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If A B and B C , then A C
Answer:
Let A ⊂ B and B ⊂ C
There be a element x such that
Let, x A
x B ( Because A B )
x C ( Because B C )
Hence,the statement is true that A C
Question:2(iv) In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If A B and B C , then A C
Answer:
The given statement is false
Let , A = {1,2}
B = {3,4,5 }
C = { 1,2,6,7,8}
Here, {1,2} {3,4,5 } = A B and {3,4,5 } { 1,2,6,7,8} = B C
But , {1,2} { 1,2,6,7,8} = A C
If x A and A B , then x B
Answer:
The given statement is false,
Let x be 2
A = { 1,2,3}
B = { 4,5,6,7}
Here, 2 { 1,2,3} = x A and { 1,2,3} { 4,5,6,7} = A B
But, 2 { 4,5,6,7} implies x B
Question:2(vi) In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If A B and x B , then x A
Answer:
The given statement is true,
Let, A B and x B
Suppose, x A
Then, x B , which is contradiction to x B
Hence, x A.
Question:3 Let A, B, and C be the sets such that A B = A C and A B = A C. Show that B = C.
Answer:
Let A, B, and C be the sets such that A B = A C and A B = A C
To prove : B = C.
A B = A + B - A B = A C = A + C - A C
A + B - A B = A + C - A C
B - A B = C - A C ( since A B = A C )
B = C
Hence proved that B= C.
Question:4 Show that the following four conditions are equivalent :
(i) A B(ii) A – B = (iii) A B = B (iv) A B = A
Answer:
First, we need to show A B A – B =
Let A B
To prove : A – B =
Suppose A – B
this means, x A and x B , which is not possible as A B .
SO, A – B = .
Hence, A B A – B = .
Now, let A – B =
To prove : A B
Suppose, x A
A – B = so x B
Since, x A and x B and A – B = so A B
Hence, A B A – B = .
Let A B
To prove : A B = B
We can say B A B
Suppose, x A B
means x A or x B
If x A
since A B so x B
Hence, A B = B
and If x B then also A B = B.
Now, let A B = B
To prove : A B
Suppose : x A
A A B so x A B
A B = B so x B
Hence,A B
ALSO, A B A B = B
NOW, we need to show A B A B = A
Let A B
To prove : A B = A
Suppose : x A
We know A B A
x A B Also ,A A B
Hence, A B = A
Let A B = A
To prove : A B
Suppose : x A
x A B ( replacing A by A B )
x A and x B
A B
A B A B = A
Question:5 Show that if A B, then C – B C – A.
Answer:
Given , A B
To prove : C – B C – A
Let, x C - B means x C but x B
A B so x C but x A i.e. x C - A
Hence, C – B C – A
Question:6 Assume that P ( A ) = P ( B ). Show that A = B
Answer:
Given, P ( A ) = P ( B )
To prove : A = B
Let, x A
A P ( A ) = P ( B )
For some C P ( B ) , x C
Here, C B
Therefore, x B and A B
Similarly we can say B A.
Hence, A = B
Question:7 Is it true that for any sets A and B, P ( A ) ∪ P ( B ) = P ( A ∪ B )? Justify your answer.
Answer:
No, it is false.
To prove : P ( A ) ∪ P ( B ) P ( A ∪ B )
Let, A = {1,3} and B = {3,4}
A B = {1,3,4}
P(A) = { { },{1},{3},{1,3}}
P(B) = { { },{3},{4},{3,4}}
L.H.S = P(A) P(B) = { { },{1},{3},{1,3},{3,4},{4}}
R.H.S.= P(A B) = { { },{1},{3},{1,3},{3,4},{4},{1,4},{1,3,4}}
Hence, L.H.S. R.H.S
Question:8 Show that for any sets A and B,
A = ( A B ) ( A – B ) and A ( B – A ) = ( A B )
Answer:
A = ( A B ) ( A – B )
L.H.S = A = Red coloured area R.H.S = ( A B ) ( A – B )
( A B ) = green coloured
( A – B ) = yellow coloured
( A B ) ( A – B ) = coloured part
Hence, L.H.S = R.H.S = Coloured part
A ( B – A ) = ( A B )
A = sky blue coloured
( B – A )=pink coloured
L.H.S = A ( B – A ) = sky blue coloured + pink coloured
R.H.S = ( A B ) = brown coloured part
L.H.S = R.H.S = Coloured part
Question:9(i) Using properties of sets, show that
A ( A B ) = A
Answer:
(i) A ( A B ) = A
We know that A A
and A B A
A ( A B ) A
and also , A A ( A B )
Hence, A ( A B ) = A
Question:9(ii) Using properties of sets, show that
A ( A B ) = A
Answer:
This can be solved as follows
(ii) A ( A B ) = A
A ( A B ) = (A A) ( A B )
A ( A B ) = A ( A B ) { A ( A B ) = A proved in 9(i)}
A ( A B ) = A
Question:10 Show that A B = A C need not imply B = C.
Answer:
Let, A = {0,1,2}
B = {1,2,3}
C = {1,2,3,4,5}
Given, A B = A C
L.H.S : A B = {1,2}
R.H.S : A C = {1,2}
and here {1,2,3} {1,2,3,4,5} = B C.
Hence, A B = A C need not imply B = C.
Question:11 Let A and B be sets. If A X B X and A X B X for some set X, show that A B.
Answer:
Given, A X B X and A X B X
To prove: A = B
A = A (A X) (A X B X)
= A (B X)
= (A B) (A X)
= (A B) (A X )
= (A B)
B = B (B X) (A X B X)
= B (A X)
= (B A) (B X)
= (B A) (B X )
= (B A)
We know that (A B) = (B A) = A = B
Hence, A = B
Question:12 Find sets A, B and C such that A B, B C and A C are non-empty sets and A B C
Answer:
Given, A B, B C and A C are non-empty sets
To prove : A B C
Let A = {1,2}
B = {1,3}
C = {3,2}
Here, A B = {1}
B C = {3}
A C = {2}
and A B C
Answer:
n ( taking tea) = 150
n (taking coffee) = 225
n ( taking both ) = 100
n(people taking tea or coffee) = n ( taking tea) + n (taking coffee) - n ( taking both )
= 150 + 225 - 100
=375 - 100
= 275
Total students = 600
n(students taking neither tea nor coffee ) = 600 - 275 = 325
Hence,325 students were taking neither tea nor coffee.
Answer:
n (hindi ) = 100
n (english ) = 50
n(both) = 25
n(students in the group ) = n (hindi ) + n (english ) - n(both)
= 100 + 50 - 25
= 125
Hence,there are 125 students in the group.
(i) the number of people who read at least one of the newspapers.
(ii) the number of people who read exactly one newspaper.
Answer:
n(H) = 25
n(T) = 26
n(I) = 26
n(H I) = 9
n( T I ) = 8
n( H T ) = 11
n(H T I ) = 3
the number of people who read at least one of the newspapers = n(H T I) = n(H) + n(T) + n(I) - n(H I) - n( T I ) - n( H T ) + n(H T I )
= 25 + 26 + 26 - 9 - 8 - 11 + 3
= 52
Hence, 52 people who read at least one of the newspapers.
(ii) number of people who read exactly one newspaper =
the number of people who read at least one of the newspapers - n(H I) - n( T I ) - n( H T ) + 2 n(H T I )
= 52 - 9- 8 -11 + 6
= 30
Hence, 30 number of people who read exactly one newspaper .
Answer:
n(A) = 21
n(B) = 26
n(C) = 29
n( A B) = 14
n( A C) = 12
n (B C ) = 14
n( A B C) = 8
n(liked product C only) = 29 - 4 -8 - 6 = 11
11 people like only product C.
Careers360 offers creative and logical explanations and solutions for chapter 1 of Class 11 Maths, Sets, as well as a downloadable PDF of NCERT Solutions. The chapter includes the following topics and sub-topics:
1.1 Introduction: This section of class 11 maths ch 1 covers the origin, basic definition, and applications of sets.
1.2 Sets and their Representations: Students learn the exact definition of a set and how it can be represented in roster/set-builder notation and denoted using English alphabets.
1.3 The Empty Set: This topic explains when a set is considered an empty set.
1.4 Finite and Infinite Sets: This section provides definitions and examples of finite and infinite sets.
1.5 Equal Sets: Students gain an understanding of equal and unequal sets, along with solved examples.
1.6 Subsets: This section covers the main concepts of subsets, including subsets of a set of real numbers and intervals as subsets of R.
1.7 Power Set: The definition of power set, derived from the concept of subsets, is explained in this section.
1.8 Universal Set: This section uses real-life examples such as population studies to define the universal set and represent it using a letter.
1.9 Venn Diagrams: This section explains the origin and definition of a Venn diagram, as well as its use in illustrating the above topics and sub-topics.
1.10 Operations on Sets: Basic operations on sets are introduced, including union of sets, intersection of sets, and difference of sets.
1.11 Complement of a Set: This section explains the definition and properties of the complement of a set, along with examples and practice problems.
1.12 Practical Problems on Union and Intersection of Two Sets: Practice problems are provided to help students understand the union and intersection of two sets.
The chapter also includes six exercises and a miscellaneous exercise with a total of 64 questions and their solutions.
Exercise 1.1 Solutions 6 Questions
Exercise 1.2 Solutions 6 Questions
Exercise 1.3 Solutions 9 Questions
Exercise 1.4 Solutions 12 Questions
Exercise 1.5 Solutions 7 Questions
Exercise 1.6 Solutions 8 Questions
Miscellaneous Exercise On Chapter 1 Solutions 16 Questions
Students can find NCERT Solution for class 11th Maths collectively at one place.
chapter-1 | Sets |
chapter-2 | |
chapter-3 | |
chapter-4 | |
chapter-5 | |
chapter-6 | |
chapter-7 | |
chapter-8 | |
chapter-9 | |
chapter-10 | |
chapter-11 | |
chapter-12 | |
chapter-13 | |
chapter-14 | |
chapter-15 | |
chapter-16 |
To assist students in comprehending the principles of Sets covered in the class 11 chapter 1 maths CBSE Syllabus 2023, this chapter comprises six exercises and one miscellaneous exercise.
Comprehensive Coverage: NCERT Solutions provide a thorough explanation of all the topics covered in the chapter, ensuring students have a complete understanding of sets and related concepts.
Step-by-Step Solutions: The solutions offer step-by-step explanations for each exercise and example in the NCERT textbook. This helps students follow the logical progression of concepts.
Clarity and Simplicity: The solutions are presented in a clear and simple language to make it easy for students to comprehend complex concepts related to sets.
Happy Reading !!!
Chapter 1 of NCERT Solutions for Class 11 Maths covers the following topics:
Most students consider permutation and combination, trigonometry as the most difficult chapter in the class 11 maths but with consistent practice and the right strategy, they will get command of them also. students can take help from NCERT textbooks, exercises, and solutions. Careers360 provides these solutions freely.
Here you will get the detailed NCERT solutions for class 11 maths by clicking on the link. students can also find class 11 maths chapter 1 NCERT solutions above in the article that are listed subject-wise and chapter-wise.
ch 1 maths class 11 sets find extensive applications not only in Mathematics but also in real-life scenarios. They are widely used in various branches of Mathematics such as topology, calculus, algebra (including fields, rings, and groups), and geometry. Additionally, sets are also employed in several other fields like Physics, Chemistry, Electrical Engineering, Computer Science, and Biology.
It is very important to practice sets class 11 solutions as concepts are foundation for higher class topics such as relation and function, probability, permutation and combinations. for ease students can study class 11 maths chapter 1 pdf both offline and online mode.
Database professionals use software to store and organise data such as financial information, and customer shipping records. Individuals who opt for a career as data administrators ensure that data is available for users and secured from unauthorised sales. DB administrators may work in various types of industries. It may involve computer systems design, service firms, insurance companies, banks and hospitals.
The field of biomedical engineering opens up a universe of expert chances. An Individual in the biomedical engineering career path work in the field of engineering as well as medicine, in order to find out solutions to common problems of the two fields. The biomedical engineering job opportunities are to collaborate with doctors and researchers to develop medical systems, equipment, or devices that can solve clinical problems. Here we will be discussing jobs after biomedical engineering, how to get a job in biomedical engineering, biomedical engineering scope, and salary.
A career as ethical hacker involves various challenges and provides lucrative opportunities in the digital era where every giant business and startup owns its cyberspace on the world wide web. Individuals in the ethical hacker career path try to find the vulnerabilities in the cyber system to get its authority. If he or she succeeds in it then he or she gets its illegal authority. Individuals in the ethical hacker career path then steal information or delete the file that could affect the business, functioning, or services of the organization.
GIS officer work on various GIS software to conduct a study and gather spatial and non-spatial information. GIS experts update the GIS data and maintain it. The databases include aerial or satellite imagery, latitudinal and longitudinal coordinates, and manually digitized images of maps. In a career as GIS expert, one is responsible for creating online and mobile maps.
The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.
Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.
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If you are intrigued by the programming world and are interested in developing communications networks then a career as database architect may be a good option for you. Data architect roles and responsibilities include building design models for data communication networks. Wide Area Networks (WANs), local area networks (LANs), and intranets are included in the database networks. It is expected that database architects will have in-depth knowledge of a company's business to develop a network to fulfil the requirements of the organisation. Stay tuned as we look at the larger picture and give you more information on what is db architecture, why you should pursue database architecture, what to expect from such a degree and what your job opportunities will be after graduation. Here, we will be discussing how to become a data architect. Students can visit NIT Trichy, IIT Kharagpur, JMI New Delhi.
Individuals who opt for a career as a remote sensing technician possess unique personalities. Remote sensing analysts seem to be rational human beings, they are strong, independent, persistent, sincere, realistic and resourceful. Some of them are analytical as well, which means they are intelligent, introspective and inquisitive.
Remote sensing scientists use remote sensing technology to support scientists in fields such as community planning, flight planning or the management of natural resources. Analysing data collected from aircraft, satellites or ground-based platforms using statistical analysis software, image analysis software or Geographic Information Systems (GIS) is a significant part of their work. Do you want to learn how to become remote sensing technician? There's no need to be concerned; we've devised a simple remote sensing technician career path for you. Scroll through the pages and read.
Budget analysis, in a nutshell, entails thoroughly analyzing the details of a financial budget. The budget analysis aims to better understand and manage revenue. Budget analysts assist in the achievement of financial targets, the preservation of profitability, and the pursuit of long-term growth for a business. Budget analysts generally have a bachelor's degree in accounting, finance, economics, or a closely related field. Knowledge of Financial Management is of prime importance in this career.
The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.
Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.
An underwriter is a person who assesses and evaluates the risk of insurance in his or her field like mortgage, loan, health policy, investment, and so on and so forth. The underwriter career path does involve risks as analysing the risks means finding out if there is a way for the insurance underwriter jobs to recover the money from its clients. If the risk turns out to be too much for the company then in the future it is an underwriter who will be held accountable for it. Therefore, one must carry out his or her job with a lot of attention and diligence.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
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Individuals who opt for a career as a stock analyst examine the company's investments makes decisions and keep track of financial securities. The nature of such investments will differ from one business to the next. Individuals in the stock analyst career use data mining to forecast a company's profits and revenues, advise clients on whether to buy or sell, participate in seminars, and discussing financial matters with executives and evaluate annual reports.
A Researcher is a professional who is responsible for collecting data and information by reviewing the literature and conducting experiments and surveys. He or she uses various methodological processes to provide accurate data and information that is utilised by academicians and other industry professionals. Here, we will discuss what is a researcher, the researcher's salary, types of researchers.
Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.
A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.
Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems.
A Safety Manager is a professional responsible for employee’s safety at work. He or she plans, implements and oversees the company’s employee safety. A Safety Manager ensures compliance and adherence to Occupational Health and Safety (OHS) guidelines.
A Conservation Architect is a professional responsible for conserving and restoring buildings or monuments having a historic value. He or she applies techniques to document and stabilise the object’s state without any further damage. A Conservation Architect restores the monuments and heritage buildings to bring them back to their original state.
A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software.
Highway Engineer Job Description: A Highway Engineer is a civil engineer who specialises in planning and building thousands of miles of roads that support connectivity and allow transportation across the country. He or she ensures that traffic management schemes are effectively planned concerning economic sustainability and successful implementation.
Are you searching for a Field Surveyor Job Description? A Field Surveyor is a professional responsible for conducting field surveys for various places or geographical conditions. He or she collects the required data and information as per the instructions given by senior officials.
Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.
A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.
Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth.
The audiologist career involves audiology professionals who are responsible to treat hearing loss and proactively preventing the relevant damage. Individuals who opt for a career as an audiologist use various testing strategies with the aim to determine if someone has a normal sensitivity to sounds or not. After the identification of hearing loss, a hearing doctor is required to determine which sections of the hearing are affected, to what extent they are affected, and where the wound causing the hearing loss is found. As soon as the hearing loss is identified, the patients are provided with recommendations for interventions and rehabilitation such as hearing aids, cochlear implants, and appropriate medical referrals. While audiology is a branch of science that studies and researches hearing, balance, and related disorders.
An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.
Are you searching for an ‘Anatomist job description’? An Anatomist is a research professional who applies the laws of biological science to determine the ability of bodies of various living organisms including animals and humans to regenerate the damaged or destroyed organs. If you want to know what does an anatomist do, then read the entire article, where we will answer all your questions.
For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs.
Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.
Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.
Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.
Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.
A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.
The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.
A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.
Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.
An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story.
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In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.
In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion.
Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article.
For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.
Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.
Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.
Individuals who opt for a career as a reporter may often be at work on national holidays and festivities. He or she pitches various story ideas and covers news stories in risky situations. Students can pursue a BMC (Bachelor of Mass Communication), B.M.M. (Bachelor of Mass Media), or MAJMC (MA in Journalism and Mass Communication) to become a reporter. While we sit at home reporters travel to locations to collect information that carries a news value.
Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.
A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications.
Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.
A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.
A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans.
A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software.
The Process Development Engineers design, implement, manufacture, mine, and other production systems using technical knowledge and expertise in the industry. They use computer modeling software to test technologies and machinery. An individual who is opting career as Process Development Engineer is responsible for developing cost-effective and efficient processes. They also monitor the production process and ensure it functions smoothly and efficiently.
An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party.
An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems.
Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack
An Automation Test Engineer job involves executing automated test scripts. He or she identifies the project’s problems and troubleshoots them. The role involves documenting the defect using management tools. He or she works with the application team in order to resolve any issues arising during the testing process.
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